Sharp Partial Identification for Survival Model Comparison Without Target Outcomes

Abstract

We compare two locked survival prediction models in a target population before target survival outcomes are available. At a prespecified horizon, the estimand is the target Brier-risk contrast. Under a bounded conditional log-odds shift model on a prespecified deployment summary, we derive a sharp identified set preserving the shared unidentified target outcome law. Direct identification is never wider than separately identifying the risks and subtracting their bounds, with strict tightening under a Brier-specific same-side-1/2 condition. For right-censored source data, conditional Cox censoring estimation, inverse-probability-of-censoring-weighted logistic outcome modeling, and a joint pairs bootstrap yield simultaneous confidence envelopes over a finite sensitivity grid. In simulations, separate-to-direct width ratios ranged from 1.00 to 5.73 across controlled prediction geometries. Targeted simulations showed finite-sample undercoverage of the outer envelope at the small, heavily censored non-small-cell lung cancer (NSCLC) information scale (0.847-0.861 versus 0.95 nominal), compared with 0.946 at the Rotterdam-GBSG scale. In the cross-institutional NSCLC application, all 40 prespecified evaluations resulted in DEFER despite reduced identification uncertainty. In a supporting Rotterdam-to-GBSG analysis, candidate superiority was certified under small sensitivity allowances; one locked configuration yielded ADOPT CANDIDATE under direct identification but DEFER under separate-risk subtraction. Direct identification can materially reduce identification uncertainty and change the operational conclusion when signal and sampling precision are sufficient, while retaining DEFER when directional certification is unsupported.